<PAGE>

                             Pure Resources, Inc.

                                 Exhibit 10.10
                                 -------------

Letter Agreement, dated June 22, 2000, among Titan Exploration, Inc., Chase Bank
of Texas, N.A., and Financial Institutions now and thereafter parties thereto.


<PAGE>

                                                                  EXHIBIT 10.10

                                 June 22, 2000



To the Banks and Financial Institutions
Listed on Schedule 1 Hereto

     Re:  Credit Agreement dated as of June 24, 1999 (as amended to date, the
          "Credit Agreement") among Titan Exploration, Inc., as Borrower
          ("Borrower"), Chase Bank of Texas, National Association, as Agent, and
          the Lenders Signatory Thereto

Ladies and Gentlemen:

     Reference is made to the Credit Agreement for the meanings of terms defined
therein which, unless otherwise defined in this letter, shall have the same
meanings when used herein.

     Last December, Agent and Lenders agreed with Borrower to extend the
Maturity Date under the Credit Agreement to April 1, 2001.  Borrower now
requests Lenders' and Agent's agreement that the term "Maturity Date" in the
Credit Agreement will hereafter refer to July 1, 2001 rather than April 1, 2001.

     Please execute a copy of this letter in the space provided below to
evidence this  requested agreement.  Thank you very much for your cooperation.

                         Yours truly,

                         TITAN EXPLORATION, INC.


                         By:/s/ John L. Benfatti
                            --------------------
                            Name: John L. Benfatti
                            Title: Vice President - Accounting & Controller
<PAGE>

AGREED TO as of the date first written above:

CHASE BANK OF TEXAS, NATIONAL
 ASSOCIATION
Individually, as Issuing Bank, and as
Administrative Agent


By: /s/ Robert C. Mertensotto
   --------------------------
   Name: Robert C. Mertensotto
   Title: Managing Director

FIRST UNION NATIONAL BANK, Individually
and as Documentation Agent


By: /s/ David Humphreys
   --------------------
   Name: David Humphreys
   Title: Vice President

MORGAN GUARANTY TRUST COMPANY OF NEW YORK,
Individually and as Syndication Agent


By: /s/ Colleen Galle
   ------------------
   Name: Colleen Galle
   Title: Vice President

CREDIT LYONNAIS NEW YORK BRANCH


By: /s/ Philippe Soustra
   ---------------------
   Name: Philippe Soustra
   Title: Senior Vice President

BANK ONE, TEXAS, N.A.


By: /s/ Wm. Mark Cranmer
   ---------------------
   Name: Wm. Mark Cranmer
   Title: Vice President
<PAGE>

PARIBAS


By: /s/ Brian Malone
   -----------------
   Name: Brian Malone
   Title: Director

UNION BANK OF CALIFORNIA, N.A.


By: /s/ Gary Shekerjian
   --------------------
   Name: Gary Shekerjian
   Title: Vice President
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                                 SCHEDULE 1


Chase Bank of Texas, N.A.
One Chase Manhattan Plaza, 8th Floor
New York, NY 10081
Attention: Muniram Appanna Agency Services

First Union National Bank
c/o First Union Corporation
1001 Fannin Street, Suite 2255
Houston, Texas 77002-6709
Attention: Ms. Vicki Crispens

Morgan Guaranty Trust
 Company of New York
60 Wall Street
New York, New York 10260
Attention: Phillip McNeal

Credit Lyonnais New York Branch
c/o Credit Lyonnais
Houston Representative Office
1000 Louisiana, Suite 5360
Houston, Texas 77002
Attention: John M. Falbo

Bank One, Texas, N.A.
1717 Main Street
Dallas, Texas 75201
Attention: Mark Cranmer

Paribas
1200 Smith Street, Suite 3100
Houston, Texas 77002
Attention:  Brian Malone
<PAGE>

Union Bank of California, N.A.
4200 Lincoln Plaza
500 North Akard
Dallas, Texas 75201
Attention: Gary Shekerjian

cc:  Chase Securities, Inc.
     707 Travis Street, 5N86
     Houston, Texas 77002
     Attention: Robert C. Mertensotto